Calculus Post

Okay before I start my blog I want to address something...

Just because B-Rob is gone, it does not mean that we are done practicing for the AP. Even if the AP is not important to you guys, I know it is important to some of us taking the course...so

Please, make sure you are doing your work and being quiet in class for others so they can get help with questions and finish out their corrections.

Anyway, as to what I will explain...

Some people are still confusing a few things about position, velocity, and acceleration.

The order is, like I said, position, velocity, and acceleration. So, if you are given the velocity function and it says to find the distance traveled from 1 to 5, for example, you would integrate the velocity function from 1 to 5. If you are given velocity and are asked to find the acceleration function, you would take the derivative of velocity. These questions are almost always a give-a-way and are really easy points to get.

When you are doing integration, you really need to have a mindset or an eye that looks for something in the problem that has it's derivative elsewhere. It doesn't have to be the exact derivative but it just needs to be similar.

Also, don't forget that you can manipulate the equation in whatever way possible before taking the integral...

For example, you wouldn't leave e^x(e^(3x) and try to integrate that. You would first combine the two by adding their exponents to get e^(4x) and then integrate that. Manipulating the problem will save you heaps of time.

Also for all of those problems where it gives you like a piecewise-function and it says to make this function continous and differentiable, what value of a or b or whatever variable they give you...

The way you do this is plug in the bounds that it's around..it will usually be by a number...

Then you take the derivative and plug in the bounds you just plugged in....and now you have two equations which is a system of equations. Now all you need to do is solve the system by whatever method you like best. I usually find when you have two variables...just solving each in terms of one variable works best because you can just set them equal and solve for the other one, then just plug that answer back in one of the others to get the other variable.

Anyway, enjoy your day off.